Assume the mostly infrared radiation from a heat lamp acts like a continuous wav

Question

Assume the mostly infrared radiation from a heat lamp acts like a continuous wave with wavelength 1.50 µm.

(a) If the lamp's 200 W output is focused on a person's shoulder, over a circular area 22.5 cm in diameter, what is the intensity?

(b) What is the peak electric field strength? kV/m

(c) Find the peak magnetic field strength. µT

(d) How long will it take to increase the temperature of the 4.00 kg shoulder by 2.00°C, assuming no other heat transfer and given its specific heat is 0.830 kcal/kg·°C?

Explanation / Answer

part A : apply formula for Intensity I = power/area = Emax^2/2uoC

where Emax = B*c

C is speed of light

B is magnetic field

uo is 4pi e-7

Area A = 4pi r^2

so

I = 200/(4*3.14 * 0.1125 * 0.1125)

I = 1.258 KW/m^2

---------------------------

Emax^2 = 2uoC* I

Emax^2 = 2* 4*3.14 e -7 * 3e8 * 1258.158

Emax = 0.973 KV/m

--------------------------------------

as B = E/c

peak magnetic B = 973.72 /(3e8)

B = 3.24 uT

-----------------------------------------------------

Power P = Q/t

time t = Q/P

t = McDT/P

t = 4 * 0.830*1000 * 2/(200)

t = 33.2 secs

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